This is how it goes....
The brick heat riser is the is the internal brick chimney. Then the black tube, which is the metal insides of a electric hot water heater, is placed around the brick chimney. The gap between the black tube and the brick is filled with an insulation mineral. I'm using perlite at about 2 R per inch. Then the 55 gallon barrel is placed on top of that chimney assembly and sealed up. The horizontal stove pipe ( not pictured ) is connected to the barrel with a clean out and primer. The stove pipe is embedded in cob or some other thermal mass for heat storage. Then the pipe runs out of the building.